arXiv subjects

Shin'ichi Nojiri

Publications and source records attributed to Shin'ichi Nojiri.

At least 37 records · Page 2Linked to original sources

arXiv2025

The correspondence of generalised entropic cosmology theory with $F(T)$ and $F(Q)$ modified gravity and gravitational waves

We investigate the correspondence between modified gravity theories and general entropic cosmology theory. Such a theory is proposed by an analogy with Jacobson's work, where the Einstein equation was derived from the Bekenstein-Hawking entropy. We compare FLRW equations obtained in entropic gravity with those in modified gravity theories. It is found the correspondence of $F(T)$ and $F(Q)$ gravities and general entropic gravity. We regard the $F(T)$ and $F(Q)$ gravity theories as effective local theories corresponding to the entropic gravity theories and we investigate the gravitational waves. The obtained equation of the gravitational wave is identical to that in Einstein's gravity except that the gravitational coupling is modified by the functional form of the functions $F(T)$ and $F(Q)$. It is interesting that in the case of the Tsallis entropic cosmology, the gravitational coupling becomes small or large, which may suppress or enhance the emission of the gravitational wave.

gr-qc↗

arXiv2025

Non-metricity approach to Jackiw-Teitelboim gravity

We construct 2d Jackiw-Teitelboim (JT) gravity in the framework of symmetric teleparallel gravity based on a non-metricity tensor. In symmetric teleparallel gravity, we often use the scalar quantity $Q$ composed of the bilinear terms of the non-metricity tensor but $Q$ is not a unique scalar quantity from the viewpoint of covariance. However, other scalar quantities composed of the non-metricity tensor generate ghosts in general. In two dimensions, because a propagating gravitational mode does not exist, if we consider general scalar quantities, there might appear any propagating modes although these modes are often ghosts. We consider a general combination of the terms given by the bi-linear of the non-metricity tensors. After finding the condition that the conformal form of the metric is compatible with the coincident gauge, where connections vanish, we determine the combination so that a solution with constant curvature exists. The obtained model corresponds to 2d JT gravity in the framework of the symmetric teleparallel gravity. The conformal mode propagates as a scalar in this theory and we also consider the condition that the scalar mode is not a ghost.

hep-th↗

arXiv2025

Black Holes Thermodynamics and Generalised Non-Extensive Entropy

The first part of this work provides a review of recent research on generalised entropies and their origin, as well as its application to black hole thermodynamics. To start, it is shown that the Hawking temperature and the Bekenstein-Hawking entropy are, respectively, the only possible thermodynamical temperature and entropy of the Schwarzschild black hole. Moreover, it is investigated if the other known generalised entropies, which include Rényi's entropy, the Tsallis one, and the four- and five-parameter generalised entropies, could correctly yield the Hawking temperature and the ADM mass. The possibility that generalised entropies could describe hairy black hole thermodynamics is also considered, both for the Reissner-Nordström black hole and for Einstein's gravity coupled with two scalar fields. Two possibilities are investigated, namely, the case when the ADM mass does not yield the Bekenstein-Hawking entropy, and the case in which the effective mass expressing the energy inside the horizon does not yield the Hawking temperature. For the model with two scalar fields, the radii of the photon sphere and of the black hole shadow are calculated, which gives constraints on the BH parameters. These constraints are seen to be consistent, provided the black hole is of Schwarzschild type. Subsequently, the origin of the generalised entropies is investigated, by using their microscopic particle descriptions in the frameworks of a microcanonical and of a canonical ensemble, respectively. To finish, the McLaughlin expansion for the generalised entropies is used to derive, in each case, the microscopic interpretation of the generalised entropies, via the canonical and the grand canonical ensembles.

gr-qc↗

arXiv2024

Black holes and their shadows in $F(R)$ gravity

We investigate the radii of the photon sphere and the black hole shadow in the framework of $F(R)$ gravity. For this purpose, we derive the field equation for the corresponding theory when the general spherically symmetric and static configuration is considered. This equation is the third-order differential equation with respect to $F_R(r)\equiv \left. \frac{dF(R)}{dR}\right|_{R=R(r)}$, where $r$ is the radial coordinate. Solving the equation, we find $F(R)$ as a function of $r$, $F_R=F_R(r)$. By using the assumed and obtained geometry, one can calculate the scalar curvature $R$ as a function of $r$, $R=R(r)$, which could be solved with respect to $r$ as $r=r(R)$. Then one finds the functional form of $F_R$ as a function of the scalar curvature $R$, $F_R=F_R(R)=F_R\left( r=r\left(R\right)\right)$.

gr-qc↗

arXiv2024

Compact star in noninteger power model of $f(R)$ gravity

We investigate compact stars in the noninteger power (NIP) model of $f(R)$ gravity theory, which includes the higher-curvature correction to the Einstein-Hilbert action. The mass-radius relation of the compact stars in the NIP model predicts large deviations from those in the general relativity in the low-mass region, potentially allowing us to test the NIP model by future astrophysical observations. We also study the nonvanishing scalar hair surrounding the compact star and demonstrate that the chameleon mechanism works efficiently. They result in distinct scalar profiles inside and outside the star, which implies screening the fifth force mediated by the scalar field.

gr-qc↗

arXiv2024

Black holes, photon sphere, and cosmology in ghost-free $f(\mathcal{G})$ gravity

The improved version of ghost-free $f(\mathcal{G})$ gravity introduced in Phys.~Lett.~B \textbf{631} (2005), 1-6 is proposed and investigated. It is demonstrated that improved ghost-free $f(\mathcal{G})$ gravity may be consistently applied to describe the expanding universe (with horizon) as well as the static spacetime like black holes. Interestingly, such a theory looks like a close avatar of scalar-Einstein-Gauss-Bonnet gravity with the only difference that the scalar field is not a dynamical one so that many predictions of ghost-free $f(\mathcal{G})$ gravity are very similar to that of sEGB gravity. We discuss the gravitational wave in the improved model with the condition that the propagating speed of the gravitational wave is identical to that of the propagation speed of light. A model that describes inflation in the early universe and could satisfy the observational constraints is also constructed. The solution of ghost-free $f(\mathcal{G})$ gravity realising the given static spacetime with spherical symmetry is proposed. Some of such solutions realise explicitly the Reissner-Nordström black hole or the Hayward black hole, which is a regular black hole without curvature singularity, We also construct a black hole in our theory which contains the Arnowitt-Deser-Misner (ADM) mass, the horizon radius, and the radius of the photon sphere as independent parameters. The radius of the black hole shadow in this model as well as photon sphere radius are estimated. It is shown that there exists a parameter region which satisfies the constraints coming from Event Horizon Telescope observations. Furthermore, we construct model where the radius of the black hole shadow or photon orbit is smaller than the horizon radius supposed from the ADM mass.

gr-qc↗

arXiv2024

Gravitational collapse, primordial black hole, and gravitational wave in Einstein--Gauss-Bonnet theory with two scalar fields

In this paper, we investigate the gravitational collapse to form the black hole in the acceleratingly expanding universe in the frame of Einstein--Gauss-Bonnet theory having two scalar fields and we study the propagation of the gravitational wave (GW). This may describe the creation of the primordial black holes in the early stages of the universe and the impact of their creation on the propagation of primordial gravitational waves. The collapsing spacetime can be obtained by using the formulation of the ``reconstruction'', that is, we find a model that realises the desired or given geometry. In the reconstructed models, ghosts often appear, which could be eliminated by imposing constraints. We show that the standard cosmological solutions or self-gravitating objects such as a planet, the Sun, various types of stars, etc., in Einstein's gravity, are also solutions in this model. Using the dynamical value of the Gauss-Bonnet coupling, the propagation of the high-frequency GW is investigated. The propagating speed changes due to the coupling during the period of the black hole formation. The speed of the GW propagation going into the black hole is different from that of the wave going out.

gr-qc↗

arXiv2024

Improving Mimetic Gravity with Non-trivial Scalar Potential: Cosmology, Black Holes, Shadow and Photon Sphere

It is not easy to treat the spacetime with horizon(s) in the standard mimetic gravity. The solution to this problem has been presented in Phys.~Lett.~B 830 (2022), 137140, where it was suggested to modify the Lagrange multiplier constraint. In this paper, by using the improved formulation, we investigate the cosmology and black holes in mimetic gravity with scalar potential and in the scalar mimetic $F(R)$ gravity. The inflationary era and dark energy epoch for the above theories are presented as specific examples from the general reconstruction scheme which permits to realise any universe expansion history via the choice of the corresponding scalar potential or function $F(R)$. Two black hole solutions including the Schwarzschild and Hayward ones are constructed. The shadow and the radius of the photon sphere for the above black holes are found. The explicit confrontation of the black hole shadow radius with the observational bounds from M87$^*$ and Sgr A$^*$ objects is done. It is demonstrated that they do not conflict with Event Horizon Telescope observations.

gr-qc↗

arXiv2024

General geometry realized by four-scalar model and application to $f(Q)$ gravity

In this paper, we propose a model including four scalar fields coupled with general gravity theories, which is a generalization of the two-scalar model proposed in Phys. Rev. D \textbf{103} (2021) no.4, 044055, where it has been shown that any given spherically symmetric static/time-dependent spacetime can be realized by using the two-scalar model. We show that by using the four-scalar model, we can construct a model that realizes any given spacetime as a solution even if the spacetime does not have a spherical symmetry or any other symmetry. We also show that by imposing constraints on the scalar fields by using the Lagrange multiplier fields, the scalar fields become non-dynamical and they do not propagate. This tells that there does not appear any sound which is usually generated by the density fluctuation of the fluid. In this sense, the model with the constraints is a most general extension of the mimetic theory in JHEP \textbf{11} (2013), 135, where there appears an effective dark matter. The dark matter is non-dynamical and it does not collapse even under gravitational force. Our model can be regarded as a general extension of any kind of fluid besides dark matter. We may consider the case that the potential of the scalar fields vanishes and the model becomes a non-linear $σ$ model. Then our formulation gives a mapping from the geometry of the spacetime to the geometry of the target space of the non-linear $σ$ model via gravity theory although the physical meaning has not been clear. We also consider the application of the model to $f(Q)$ gravity theory, which is based on a non-metricity tensor and $Q$ is a scalar quantity constructed from the non-metricity tensor. ...

gr-qc↗

arXiv2024

Future singularity in an anisotropic universe

We investigate future singularities originating from the anisotropy in the Universe. We formulate a new class of singularities in the homogeneous and anisotropic universe, comparing them with the known singularities in the homogeneous and isotropic universe. We also discuss the physical consequences of the new singularities. Moreover, we develop a novel reconstruction method for the anisotropic universe by introducing four scalar fields to reconstruct cosmological models in which future singularities appear. We present an explicit example where the anisotropy may grow in the future up to singularity.

gr-qc↗

arXiv2024

Different aspects of entropic cosmology

We give a short review of the recent developments of entropic cosmology based on two thermodynamic laws of the apparent horizon, namely the first and the second laws of thermodynamics. The first law essentially provides the change of the entropy of the apparent horizon during the cosmic evolution of the universe, in particular, it is given by: $TdS = -d(ρV) + W dV$ (where $W$ is the work density and other quantities have their usual meaning). In this way, the first law actually links various theories of gravity with the entropy of the apparent horizon. This leads to a natural question -- ``what will be the form of the horizon entropy corresponding to a general modified theory of gravity?'' The second law of horizon thermodynamics states that the change of total entropy (the sum of horizon entropy $+$ matter fields' entropy) with respect to cosmic time must be positive, where the matter fields behave like an open system characterised by a non-zero chemical potential. The second law of horizon thermodynamics importantly provides model-independent constraints on entropic parameters. Finally, we discuss the standpoint of entropic cosmology on inflation (or bounce), reheating and primordial gravitational waves from the perspective of generalised entropy function.

gr-qc↗

arXiv2024

$F(Q)$ gravity with Gauss-Bonnet corrections: from early-time inflation to late-time acceleration

We show that in the $f(Q)$ gravity with a non-metricity scalar $Q$, the curvatures in Einstein's gravity, that is, the Riemann curvature constructed from the standard Levi-Civita connection, could not be excluded or naturally appear. The first observation is that even in $f(Q)$ gravity, the conservation of the matter energy-momentum tensor is not described by the covariant derivatives in the non-metricity gravity but that is given by the Levi-Civita connection. The commutator of the covariant derivatives in Einstein's gravity inevitably induces the Riemann curvature. There is no symmetry nor principle which prohibits the Riemann curvature in non-metricity gravity. Based on this observation, we propose and investigate $f\left(Q, \mathcal{G} \right)$ gravity with the Gauss-Bonnet invariant $\mathcal{G}$ and its generalisations. We show how $f\left(Q, \mathcal{G} \right)$ models realising any given the Friedmann-Lemaître-Robertson-Walker (FLRW) spacetime can be reconstructed. We apply the reconstruction formalism to cosmology. Explicitly, the gravity models which realise slow roll or constant roll inflation, dark energy epoch as well as the unification of the inflation and dark energy are found. The dynamical autonomous system and the gravitational wave in the theory under investigation are discussed. It is found the condition that the de Sitter spacetime becomes the (stable) fixed point of the system.

gr-qc↗

arXiv2024

Extremely small stars in scalar-tensor gravity: when stellar radius is less than Schwarzschild one

We show analytically that there exist compact stellar objects akin to neutron stars whose radius is smaller than the Schwarzschild radius defined by Arnowitt-Deser-Misner (ADM) mass. The radius of the compact object is defined by the radius where the energy density and the pressure of ordinary matter vanish, while clouds of scalar(s) can extend beyond this radius -- a situation that is often encountered in modified gravity theories, like $F(R)$ gravity and the scalar--Einstein--Gauss-Bonnet gravity. The clouds of scalar mode(s) give additional contributions to the ADM mass and as a result, the corresponding Schwarzschild radius given by the ADM mass can be larger than that of the compact object.

gr-qc↗

arXiv2024

Well-defined $f(Q)$ Gravity, Reconstruction of FLRW Spacetime and Unification of Inflation with Dark Energy Epoch

We formulate the convenient and mimetic $f(Q)$ gravities in terms of the metric and four scalar fields with the $Q$ being the non-metricity scalar. As a result, it is shown that the obtained field equations are well-defined. By using the field equations, we show how the $f(Q)$ models which realise any given FLRW spacetime may be reconstructed. We construct convenient $f(Q)$ gravity and mimetic $f(Q)$ gravity, which describe the inflation and dark energy epochs and even unify the inflation and dark energy. Moreover, a radiation-dominated epoch and early dark energy may be easily included in the above theories as is explicitly shown. It is shown that the inflationary spectral index $n_s$ and the tensor-to-scalar ratio $r$ are consistent with Planck data for some models of $f(Q)$ gravity. Corresponding asymptotic forms of $f(Q)$ and mimetic $f(Q)$ are given. Finally, some remarks on possible reconstruction for spherically symmetric spacetime are given.

gr-qc↗

arXiv2024

Wormholes inside stars and black holes

We construct models of two exotic objects: (i) a wormhole whose throat is hidden by a stellar object like a neutron star; and (ii) a wormhole inside a black hole. We work within Einstein's gravity coupled to two scalar fields with a specific choice of the scalar field Lagrangian. In general, the model contains ghosts, but they are eliminated using the constraints given by the Lagrange multiplier fields. The constraints are a generalization of the mimetic constraint, where non-dynamical dark matter effectively appears. As a result, in our model, instead of the non-dynamical dark matter, non-dynamical exotic matter like a phantom effectively arises. For the mixed wormhole-plus-star system, we find the corresponding mass-radius relations and show that it is possible to get characteristics comparable to those of ordinary neutron stars. For the wormhole inside the black hole, we find an extremal limit where the radius of the throat coincides with the radius of the event horizon and demonstrate that the Hawking temperature vanishes in this limit.

gr-qc↗

arXiv2024

Gravitational waves in $f(Q)$ non-metric gravity via geodesic deviation

We investigate gravitational waves in the $f(Q)$ gravity, i.e., a geometric theory of gravity described by a non-metric compatible connection, free from torsion and curvature, known as symmetric-teleparallel gravity. We show that $f(Q)$ gravity exhibits only two massless and tensor modes. Their polarizations are transverse with helicity equal to two, exactly reproducing the plus and cross tensor modes typical of General Relativity. In order to analyze these gravitational waves, we first obtain the deviation equation of two trajectories followed by nearby freely falling point-like particles and we find it to coincide with the geodesic deviation of General Relativity. This is because the energy-momentum tensor of matter and field equations are Levi-Civita covariantly conserved and, therefore, free structure-less particles follow, also in $f(Q)$ gravity, the General Relativity geodesics. Equivalently, it is possible to show that the curves are solutions of a force equation, where an extra force term of geometric origin, due to non-metricity, modifies the autoparallel curves with respect to the non-metric connection. In summary, gravitational waves produced in non-metricity-based $f(Q)$ gravity behave as those in torsion-based $f(T)$ gravity and it is not possible to distinguish them from those of General Relativity only by wave polarization measurements. This shows that the situation is different with respect to the curvature-based $f(R)$ gravity where an additional scalar mode is always present for $f(R)\neq R$.

gr-qc↗

arXiv2024

Stable gravastar with large surface redshift in Einstein's gravity with two scalar fields

We propose a class of models, in which stable gravastar with large surface redshift becomes a solution. In recent decades, gravastars have become a plausible substitute for black holes. Researchers have explored stable gravastar models in various alternative gravity theories, in addition to the conventional framework of general relativity. In this paper, we present a stellar model within the framework of Einstein's gravity with two scalar fields, in accordance with the conjecture proposed by Mazur and Mottola [Proc. Nat. Acad. Sci. \textbf{101} (2004), 9545-9550]. In the model, the two scalar fields become non-dynamical by imposing constraints in order to avoid ghosts. The gravastar comprises two distinct regions, namely: (a) the interior region and (b) the exterior region. We assume the interior region consists of the de Sitter spacetime, and the exterior region is the Schwarzschild one. The two regions are connected with each other by the shell region. On the shell, we assume that the metric is given by a polynomial function of the radial coordinate $r$. The function has six constants. These constants are fixed by the smooth junction conditions, i.e., the interior region with the interior layer of the shell and the exterior region with the exterior layer of the shell. From these boundary conditions, we are able to write the coefficients of the scalar fields in terms of the interior radius and exterior radius. To clarify the philosophy of this study, we also give two examples of spacetimes that asymptote as the de Sitter spacetime for small $r$ and as the Schwarzschild spacetime for large $r$. Exploration is focused on the physical attribute of the shell region, specifically, its proper length.

gr-qc↗

arXiv2024

Horizon entropy consistent with FLRW equations for general modified theories of gravity and for all EoS of the matter field

The question that continues to hinge the interrelation between cosmology and thermodynamics is broadly described as -- what is the form of horizon entropy that links the Friedmann equations for a "$general$" gravity theory with the underlying thermodynamics of the apparent horizon? The answer to this question was known only for Einstein's gravity and for $(n+1)$ dimensional Gauss-Bonnet gravity theory, but not for a general modified theory of gravity (for instance, the $F(R)$ gravity). In the present work, we take this issue and determine a general form of entropy that connects the Friedmann equations for any gravity theory with the apparent horizon thermodynamics given by $TdS = -dE + WdV$ (the symbols have their usual meaning in the context of entropic cosmology and $W = \left(ρ- p\right)/2$ is the work density of the matter fields represented by $ρ$ and $p$ as the energy density and the pressure, respectively). Using such generalized entropy, we find the respective entropies for several modified theories of gravity (including the $F(R)$ gravity). Further, it turns out that besides the above-mentioned question, the thermodynamic law $TdS = -dE + WdV$ itself has some serious difficulties for certain values of $ω$ (the EoS of matter field). Thus we propose a modified thermodynamic law of apparent horizon, given by $TdS = -dE + ρdV$, that is interestingly free from such difficulties. The modified law proves to be valid for all EoS of the matter field and thus is considered to be more general compared to the previous one which, however, is a limiting case of the modified law for $p = -ρ$. Based on such modified thermodynamics, we further determine a generalized entropy that can provide the Friedmann equations of any general gravity theory for all values of EoS of the matter field. The further implications are discussed.

gr-qc↗